Dear oh dear iouae:
2 Kings 16:6
At that time Rezin king of Syria recovered Elath to Syria, and drove the Jews from Elath: and the Syrians came to Elath, and dwelt there unto this day.
In the original Hebrew 'Jew' is shown to come from the word 'Judean' because Jews are from Judah, which is the tribal land given to Judah son of Jacob:
http://www.scripture4all.org/OnlineInterlinear/OTpdf/2kg16.pdf
Joshua 15
1The allotment for the tribe of Judah, according to its clans, extended down to the territory of Edom, to the Desert of Zin in the extreme south.
Matthew 1
1 This is the genealogy of Jesus the Messiah the son of David, the son of Abraham: 2 Abraham was the father of Isaac, Isaac the father of Jacob, Jacob the father of Judah and his brother.
John 4:22
You Samaritans worship what you do not know; we worship what we do know, for salvation is from the Jews.
Matthew 27:37
Above his head they placed the written charge against him: this is Jesus, the king of the Jews.
Jesus was a Jew because He was of the tribe of Judah from where the name Jew is derived from. This is the Word of God but you seem to prefer the Israeli immigration department's definition; 'who will accept an application for Israeli citizenship if there is proven documentation that any grandparent—not just the maternal grandmother—was Jewish. This does not mean that person is an "ethnic Jew", but Israeli immigration will accept that person because he or she has an ethnically Jewish connection, and because this same degree of connection was sufficient to be persecuted as a Jew by the Nazis.' (Because this is what Hitler also thought)
https://en.wikipedia.org/wiki/Who_is_a_Jew?
In fact I have recently read that the rules on immigration may soon incorporate DNA testing, this is because the Israeli government need to now find a way of further reducing and controlling who they let in, in other words become even more selective.